Infinity minus an infinity yields logically impossible scenarios. Notably, one can take away identical quantities from identical quantities and arrive at contradictory remainders.

On the face of it, this claim appeals to our intuitive understanding of subtraction. If I were to claim that there exists some Integer, , such that and , then we stumble upon the contradiction that . Subtracting identical quantities from identical quantities should yield identical results.

In general, I attempt to avoid topics of morality in my discussions of theology and religion. This is not because I think the topic is too difficult or too complex to discuss, but rather because it seems like an exercise in futility to argue about morality when the foundational metaphysical views upon which we frame morality differ so greatly. I’ve found that such discussions very frequently either end up with one person expounding on the virtues of apples while the other extols the dangers of oranges; or else they end up regressing backward until we are discussing the foundational metaphysics instead of the moral topic.

However, today, I’m going to break that trend. I was recently directed to an article written in November of 2017 entitled Nine Points about Biblical Slavery and Skeptics’ Condemnation of the Bible. The author of the article intends the piece to be a defense of the Bible against complaints regarding the manner in which its constituent documents treat the institution of slavery. The topic is an understandably sore one for a great number of people. Opponents of religion are quite often quick to point out that the Ten Commandments, a list of some of the supposed most important tenets of morality, includes things like, “Keep the Sabbath holy” and “Honor thy father and mother,” but omits something like, “Thou shalt not own another person as your property.” In fact, the Bible never offers any clear proscription against slavery, and indeed seems to sanction the practice in a number of places. Given the incredibly strong modern moral aversion to the idea of slavery, Christian apologists have attempted to take up the task of showing that these modern detractors hold deep misunderstandings of what the Bible actually says about slavery.

The reason I’m breaking my usual avoidance of topics of morality to discuss this one is that I honestly don’t care about the metaphysical foundations of our ethics, in regards to slavery. All I care about, regarding this topic, are the answers to two, simple questions.

Is it morally acceptable to own another human being as property? Does the Bible sanction the owning of another human being as property?

On a blog called Theolocast, Christian apologist Todd Clay recently published an article entitled “31 Reasons to Believe in the God of the Bible.” In the article, Mr. Clay discusses a plethora of different ideas by which he claims that “the God of the Bible has made himself obvious to the world.”

Despite Todd Clay’s assertions, God’s existence is still not obvious to me. In fact, the arguments which he presents are quite bad. Indeed, it seems to me that he is claiming to have found Jesus in his philosophical toast.

In his seminal work, Summa Theologica, the celebrated Christian philosopher, Thomas Aquinas, engages with the question of the existence of God. He notes that there are certainly objections to the claim that there exists such a divinity, but Aquinas believes that these objections can be overcome and that this existence can be shown to be well-founded. The eminent philosopher then lays out a list of arguments which he supposes to make this case. These arguments have come to be known as Aquinas’ Five Ways, and they have been so influential in philosophy that many theologians and apologists still cite them as if they are authoritative logical proofs, more than 700 years after the Italian priest set them to page. On the contrary, however, it seems that there are a number of issues which prevent Aquinas’ Five Ways from being quite so powerful, now, as they may have been in his own day.

One of the common claims which is utilized in arguments for the existence of God is that actual infinities cannot exist, implying that there cannot be an infinite regress of causal events in the history of the universe. If there cannot be such an infinite regress, then there must be some First Cause. Theologians then put forth other arguments attempting to show that this First Cause must be God. Blake Giunta, a Christian apologist, has constructed a very interesting and quite useful website cataloging common lines of argumentation from both sides of the debate (color coded Green for Christian arguments and Red for opposing arguments), along with citations and documentation for those claims, called BeliefMap.org. It does not take very long for a fairly cursory perusal of Belief Map to bring one to this exact claim regarding the actually infinite.

While I disagree with Mr. Giunta on many of his views, I have a great deal of respect for him and I think that his work with Belief Map is absolutely fantastic. He truly does attempt to give an irenic and charitable view to the positions of his opposition, and he does sincerely want to discuss the actual arguments being made, instead of being content to knock down Straw Men. To that end, I would like to help Mr. Giunta add to his encyclopedia of apologetics by addressing the manner in which one might answer the claims about actual infinities.

In one of my earlier posts, I addressed the Grim Reaper paradox and offered my input on a possible resolution of the thought experiment’s curious implications. However, some of my readers may have been dissatisfied with my answer, thinking that it sidestepped around the issue rather than addressing the conundrum directly. A few people asked me why I thought that obscure philosophy on the nature of Time might have any relevance to the question, in the first place. To that end, I have decided to offer a bit more clarification and to attempt to illustrate why I think the Grim Reaper paradox is inherently flawed.

Recently, I have taken to addressing William Lane Craig’s Excursus on Natural Theology podcasts. These are lessons directed at the layperson with the goal of demonstrating the rationality of theism from simple arguments. As you may infer from my previous articles, I do not think that the Excursus has come even close to meeting that goal.

Today, we will be discussing Part 17 of the Excursus. If you read my article on Part 16, you might remember that I was actually quite excited for this, due to Dr. Craig’s promise to discuss the plausibility of Design as an explanation of the universe’s fine-tuning. As I mentioned, whenever I have discussed the idea of Intelligent Design with an apologist, I have brought up this very subject. Unfortunately, I’ve only ever been met with answers about the purported improbability of chance or necessity. I’ve never been proffered any answers with positive evidence for the idea of Design, nor even with a proposed mechanism by which the Fine-Tuning of the universe could be Designed.

Early on in the discussion, Dr. Craig makes a statement with which I wholeheartedly agree:

But we cannot infer immediately to design because sometimes it can be justified to believe in an improbable explanation. You would be justified in believing in some improbable explanation just in case there were no better explanation available of the phenomenon in question…

The question we are facing now with regard to the fine-tuning of the universe is: is design a better explanation than chance or physical necessity?

Yes, this most certainly is the question! So, how does Dr. Craig answer this question? Does he define what, exactly, he means by the term “design?” Does he offer some method for differentiating something which is “designed” from something which is not “designed?” Does he then apply this standard to the question of Fine-Tuning in order to show that the constants and quantities of the universe more keenly fit into the “designed” category than the “not designed” category?

Over the past few months, I have been listening to Dr. William Lane Craig’s Excursus on Natural Theology, which is a course designed to introduce an audience to reasons for accepting the positions of theism. From time to time, I find that Dr. Craig says something so egregiously wrong that I feel I should address it, here, at Boxing Pythagoras. In two previous articles, I have discussed Dr. Craig’s misconceptions in regards to the mathematical concept of infinity, from parts 9 and 10 of his Excursus. Today, I want to focus on Part 16 of the Excursus in which Dr. Craig talks about the Fine-Tuning problem of cosmology.

Unfortunately for our esteemed theologian, his understanding of cosmology seems to be just as poor as his understanding of mathematics.

On Monday night, I called into the Catholic Answers radio program to give the reason why I am an atheist. My stated reason was that I have not been offered any convincing reasons to believe that deity exists, and the discussion quickly turned to the subject of the Cosmological family of arguments. Unfortunately, a live call-in program does not offer the best forum for back-and-forth discussion, so I wanted to take some time to respond to a number of the things which Trent Horn said, in our dialogue.

This past Monday night, the Catholic Answers Live radio show on EWTN hosted an episode in which they asked, “Why are you an Atheist?” They restricted callers to atheists or agnostics, and asked those respondents to tell the hosts, Patrick Coffin and Trent Horn, why they are either atheist or agnostic. Anyone who made it on the air would be sent a free copy of Trent Horn’s book, Answering Atheism. Curious to see how the apologists would respond to my position– and also, to be sure, looking to get a free book– I called in to the show to offer my position. The audio recording of Monday night’s discussion is available here, but for those of you who do not want to take the time to listen to the whole show, I’ve transcribed my discussion in this article.

I would like to say that it was an absolute pleasure to talk to Trent about this subject, and I found him to be utterly sincere, entirely respectful, and genuinely interested in having a dialogue. I can honestly say that, brief as it was, this was one of the most enjoyable conversations I’ve ever had with an apologist. I am very much looking forward to receiving Trent’s book, now, and I promise that I will review it here on Boxing Pythagoras.

Also, I would be remiss if I didn’t give a huge thank you to Elaine, the call screener for the show. She seemed an absolutely lovely woman, extremely kind and respectful. After my call dropped due entirely to problems on my end, she very graciously moved me back to the head of the line when I called back in.

The transcript follows, edited only slightly at the very beginning, due to my phone troubles.